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A Generic Complete Dynamic Logic for Reasoning About Purity and Effects

  • Till Mossakowski
  • Lutz Schröder
  • Sergey Goncharov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4961)

Abstract

For a number of programming languages, among them Eiffel, C, Java and Ruby, Hoare-style logics and dynamic logics have been developed. In these logics, pre- and postconditions are typically formulated using potentially effectful programs. In order to ensure that these pre- and postconditions behave like logical formulae (that is, enjoy some kind of referential transparency), a notion of purity is needed. Here, we introduce a generic framework for reasoning about purity and effects. Effects are modeled abstractly and axiomatically, using Moggi’s idea of encapsulation of effects as monads. We introduce a dynamic logic (from which, as usual, a Hoare logic can be derived) whose logical formulae are pure programs in a strong sense. We formulate a set of proof rules for this logic, and prove it to be complete with respect to a categorical semantics. Using dynamic logic, we then develop a relaxed notion of purity which allows for observationally neutral effects such writing on newly allocated memory.

Keywords

Dynamic Logic Proof Rule Terminal Object Dynamic Logic Proposition Hoare Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Till Mossakowski
    • 1
    • 2
  • Lutz Schröder
    • 1
    • 2
  • Sergey Goncharov
    • 2
  1. 1.DFKI LaboratoryBremen
  2. 2.Department of Computer ScienceUniversity of Bremen 

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